IN these times, when the old spirit of adventure seems to be missing in everyone, the story of Christopher Columbus can help us when we are "at sea". With only stars to guide him, he crossed the mighty Atlantic and gave birth to a sea of stories, one of which speaks of his experience at the gallows.

When they lowered the rope, these were his words: "In Benares (he didn't know it was Hanoi of present-day Vietnam), in the reign of Emperor Fo Hi, there was a temple with a dome that marks the centre of the world, beneath which priests moved golden discs between three diamond needles. God placed 64 gold discs, in decreasing order of their diameters, on one needle at the creation. It was said when priests had completed their task, the needles, the temple and Brahmins would crumble into dust and, with a thunder, the universe would end. Bring such a stack of disks arranged from largest on the bottom to smallest on top placed on a rod, together with two empty rods, then, move the stack from one rod to another, where moves are allowed only if they place smaller discs on top of larger discs. Execute me when the task is over."

The question for all was: What is the minimum number of moves for completing the task? How long did it take before Columbus was executed?

The 'Towers of Hanoi' puzzle is said to have been invented by E. Lucas in 1883, but it came into this world much before that, even before Columbus. The 'Towers of Hanoi' puzzle asks for the minimum number of moves required to move the stack from one rod to another, where moves are allowed only if they place smaller disks on top of larger disks.

This was a difficult problem and I received only four solutions for it, three of which were correct, one of which was absolutely correct. When confronted with this problem a certain mathematician named Gardner had said in 1957: "The problem is isomorphic to finding a Hamiltonian path on a n-hypercube." - at which he was asked to explain in English what he had said.

It would take the Grandees 2^n-1 moves to complete the task that Columbus had given them, which would keep them occupied well beyond the time when Columbus would die naturally. Columbus, therefore, was never executed; and he didn't remain at gallows either because the Grandees soon figured out that the end wasn't near. They say that Columbus sailed again.

"It will take (2^64)-1 moves to completely transfer the discs, which comes out to be 1,84,46,74,40,73,70,95,51,615 moves," says Rohit Jindal, who is absolutely correct.

Gaurav has given pretty much the same answer. Varun Jindal of Patiala says that the answer is 1,84,46,74,40,73,70,95,51,679 steps, which is like Gaurav's answer. "The answer is 192 moves," says Sapan Gupta (Full marks for trying, but, 192 moves would have given Columbus less time to live than eternity) Keep writing at The Tribune or adityarishi99@yahoo.co.in.

— Aditya Rishi